$1.$ What will be the production schedule for the next eight weeks? How much are each of the costs associated with this production plan?

$2.$ After the quarter board meeting, the Engine Manufacturing CEO would like to assess certain case$-$based scenarios to ensure that he will implement the most appropriate production plan for the next eight weeks.

First, he thinks that based on past data, the production demand for the two types of engines might not be correctly estimated. His analyst told him that a $+/-5\%$ error might have appeared when the customer estimated his own demand and passed it along to the company. How will these changes affect the production schedule?

Second, the CEO would like to see if a reduction in the safety stock could decrease even more the total costs. What will be a lower safety stock level that could enable the achievement of a much lower total cost?

Third, the board launched the idea of simultaneous production of the two types of head engines. But this will consist in the acquisition of a new equipment that will cost the company $$250,000.$ Is it worth purchasing the new manufacturing line? What conditions might not be needed anymore, if the company will decide to move forward with the equipment purchase?

$3.$ Propose further recommendations regarding the minimization of the total costs incurred by the company during the production process. $($Hint: New optimization models might be required to sustain your recommendations$)\backslash$